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Russian
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English
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Russian
Jacobian
UK
/dʒəˈkəʊ.bi.ən/
US
/dʒəˈkoʊ.bi.ən/
Translation jacobian into russian
Jacobian
Noun
UK
/dʒəˈkəʊ.bi.ən/
US
/dʒəˈkoʊ.bi.ən/
The Jacobian is used in calculus to describe the rate of change of a function.
Якобиан используется в математическом анализе для описания скорости изменения функции.
Jacobian
Adjective
UK
/dʒəˈkəʊ.bi.ən/
US
/dʒəˈkoʊ.bi.ən/
The Jacobian matrix is crucial in multivariable calculus.
Якобианская матрица имеет решающее значение в многомерном исчислении.
Definitions
Jacobian
Noun
UK
/dʒəˈkəʊ.bi.ən/
US
/dʒəˈkoʊ.bi.ən/
A determinant used in calculus to describe the rate of change of a function with respect to its variables, often used in the context of transformations and multivariable calculus.
The Jacobian of the transformation was calculated to determine the change in area under the curve.
A matrix of all first-order partial derivatives of a vector-valued function, used to describe the linear approximation of a function near a given point.
The engineer computed the Jacobian matrix to analyze the system's stability at the equilibrium point.
Jacobian
Adjective
UK
/dʒəˈkəʊ.bi.ən/
US
/dʒəˈkoʊ.bi.ən/
Relating to or characteristic of the mathematician Carl Gustav Jacob Jacobi or his work, especially in the context of mathematics involving Jacobian matrices or determinants.
The Jacobian matrix is crucial in understanding the transformation of variables in multivariable calculus.
Idioms and phrases
jacobian matrix
The Jacobian matrix is used in multivariable calculus to describe the rate of change.
Якобианская матрица
Якобианская матрица используется в многомерном исчислении для описания скорости изменения.
jacobian determinant
The Jacobian determinant is crucial for understanding volume transformations.
Якобианский детерминант
Якобианский детерминант важен для понимания объемных преобразований.
jacobian transformation
We applied a Jacobian transformation to simplify the equation.
Якобианское преобразование
Мы применили якобианское преобразование, чтобы упростить уравнение.
jacobian method
The Jacobian method can solve systems of linear equations.
Метод Якоби
Метод Якоби может решать системы линейных уравнений.
jacobian analysis
Jacobian analysis helps us understand the behavior of dynamic systems.
Якобианский анализ
Якобианский анализ помогает нам понять поведение динамических систем.